1. Field of the Invention
The present invention relates to the production of musical waveshapes by digital tone generators.
2. Description of the Prior Art
A popular tonal effect used in musical tone synthesizers is that which is generically called "ring modulation." The same fundamental frequency modification phenomenon has been known for many years in communication systems as "balanced modulation." In these modulation systems, two signals at different frequencies are combined such that the output signal contains spectral components at the sum and difference frequencies of the original two signals. In an ideal ring modulator, the output signal would have no frequency component corresponding to that of either input signals. While such an ideal ring modulator is almost impractical to build using conventional analog techniques, it is a feature of the present invention that the ideal ring modulator can be mechanized simply and economically by the use of digital system techniques.
Let the first musical signal be represented at the discrete points x.sub.1 (gh); g=1,2, . . . as a Fourier series of the form ##EQU1## where h is a fixed time interval and N.sub.1 is the number of intervals of length h in the fundamental period of x.sub.1, N.sub.1 /2 is the harmonic number; c.sub.q is the harmonic coefficient corresponding to the qth harmonic. A second musical signal having the same number of harmonic components is similarly represented as ##EQU2##
N.sub.2 is the number of intervals of length h in the fundamental period of x.sub.2. k=1,2, . . . ,N.sub.2 /2 is the harmonic number and d.sub.k is the harmonic coefficient for the second musical signal corresponding to the k'th harmonic. The ideal ring modulator creates the product y defined as EQU y = x.sub.1 (gh).multidot.x.sub.2 (gh) ##EQU3##